I'm going to give my top in Sports games, since they have had the most impact on me.
In no particular order:
Earl Weaver Baseball on Amiga. I went out and bought an Amiga the day I saw this game being demoed on it. A true sports masterpiece. I was still playing this game 5 years later.
Hardball on C64. The first baseball game with a truly immersive 3D pitching/batting interface.
Madden on Genesis
One on One-Bird vs Magic on C64 or Amiga? Truly groudbreaking animation for its time.
Need for Speed Series.
Links Golf Series
Just for good measure, I want to add two more.
High Heat Series for the PC. The mod and tweak community allowed these games to become the benchmark in baseball.
MVP Baseball 2004 PC - This game has turned out to be a very immersive baseball game. With a solid mod and tweak community backing it up, the gameplay has become the new benchmark. With the High Heat Series currently dead, I am looking for great things from EA in the future MVPs as they dial in the gameplay even more and add their great abilities for doing career/dynasty modes. The one in the current game lacks some depth and has some bugs, but it is still a great gameplay experience and can accomodate players of all skill levels. Who would have ever thought EA could do such a great baseball game after the TriplePlay crap they put out for so long.
Oops! I have to add one more because it was so well done. Oldtime Baseball for the PC. Great historical baseball experience with 3 classic announcers and beautiful oldtime stadiums with a huge stat database.
I'm going to throw my 2 cents in and say (surprise surprise) Battlefield1942. I know its nothing real groundbreaking but the fact that when playing a FPS and having many types of vehicles at your disposal changes your strategy. Most FPS games your stuck playing the same role ie: the soldier but in BF the second you decide to take a tank or a plane your no longer a soldier with a gun but now have bombs or shells and thus your whole role for the team has been changed. More and more FPS games are coming out now that have that BF flavour.
I see that no-one has mentioned Maniac Mansion which is a very influential game. This game was the first point & click game, before Maniac Mansion, games had you typing what you wanted your character to do. When Maniac Mansion was released around 1987 it took the world by storm because you were able to selecte the commands which you wanted your character to do by using a keyboard, joystick, mouse, game controller, et al.